A note on the behaviour of a two group minimum critical mass problem as the slowing down length tends to zero

It was shown by Goertzel that the condition for minimum critical mass in a thermal reactor requires the thermal flux in the core to be flat. The spatial distribution of fissile material is determined by an integral equation based on multi-group diffusion theory. In this note we make some comments on the mathematical difficulties which ensue when the slowing down length tends to zero, i.e. there is only a thermal group.